A \(k\) -OV instance \(\Phi \)  is a set \(A\subseteq \lbrace 0,1\rbrace ^{\mathbb {d}}\)  of \(n\)  binary vectors of dimension \(\mathbb {d}=\theta {(\log {n})}\)  and the \(k\) -OV problem asks if we can find \(k\)  vectors \(a_1,\ldots ,a_k\in A\)  such that they are orthogonal, i.e. \(a_1\cdot \ldots \cdot a_k=0\) . The \(k\) -OV Hypothesis says that solving \(k\) -OV requires \(n^{k-o(1)}\)  time, and it is implied by SETH [1]}, [2]}.
